Such an X-ray generator includes one disclosed in Japanese Unexamined Patent Publication No. 7 (1995)-29532. This X-ray generator includes a cathode portion which emits thermoelectrons, a grid electrode which controls the thermoelectrons emitted from the cathode portion, a target which generates X-rays by collisions of the thermoelectrons, and a voltage controller which controls voltages to be applied to the cathode portion and the grid electrode. The cathode portion includes a cathode made of porous tungsten impregnated with an excellent electron emitting material such as BaO, and a heater for heating and thereby allowing the cathode to emit the thermoelectrons.